1. Derive formulae involving backward differences for the first and second derivatives of a function.

2. The function   is tabulated for x = 1.00(0.05)1.30 to 5D:

1. Estimate the values of f'(1.00) and f"(1.00), using Newton's forward difference formula.

2. Estimate f'(1.30) and f"(1.30), using Newton's backward difference formula.

18. Find the missing value from the following table.X : 2 3 4 5 6 Y : 45.0 49.2 54.1 - 67.4

20. Form the divided difference table for the following data:X : -2 0 3 5 7 8F(x) : -792 108 -72 48 -144 -252

 ExampleThis example interpolates at the point x=0.28 from the function values

xi- 1.00 0.50 0.00 0.50 1.00 1.50 yi - 0.00 0.53 1.00 0.46 2.00 11.09 .

Find f (x) from the table below also find f (7)X : 0 1 2 3 4 5 6

F (x) : -1 3 19 53 111 199 323

For the given table of values0.1 0.2 0.3 0.4 0.5 0.6

0.425 0.475 0.400 0.452 0.525 0.575

 

, using two-point equation will be calculated as.............

 

 

 

        -0.5

        0.5

        0.75

        -0.75

Read more: MTH603 Numerical Analysis Solved Final Term MCQs Mega File - Virtual University of Pakistan http://vustudents.ning.com/group/mth603numericalanalysis/forum/topics/mth603-numerical-analysis-solved-final-term-mcqs-mega-file#ixzz2ToSWfNOk

Interpolate the value of 0.25 using Newton’s forward difference formula.

x 0.2 0.3 0.4 0.5 0.6

F(x) 0.2304 0.2788 0.3222 0.3617 0.3979

Construct a forward difference table for the following values

x 0.1 0.3 0.5 0.7 0.9 1.1 1.3

y 0.003 0.067 0.148 0.248 0.37 0.518 0.697